All terms end with 1 (the seed) and, except the third a(3), begin with 1 or 3. - Jean-Christophe Hervé, May 07 2013

Proof that 333 never appears in any a(n): suppose it appears for the first time in a(n); because of 'three 3' in 333, it would imply that 333 is also in a(n-1), which is a contradiction. - Jean-Christophe Hervé, May 09 2013